Los Angeles -LRB- CNN -RRB- -- A father and mother showed heroism when a gunman opened fired inside their California home before dawn Saturday , but two members of the family could n't overcome their wounds , Inglewood police said .

The mother ran from the house carrying her youngest child , though she was shot in both legs , in an `` extraordinary rescue attempt , '' police said . The 4-year-old boy , however , was shot in the head and later died in surgery . The mother was in critical but stable condition Saturday afternoon .

Inside the house , the father used his body as a shield in trying to protect the other three children .

Despite the father 's efforts , the gunfire wounded two of his children : a 6-year-old boy in the pelvis and a 7-year-old girl in the chest . Both were in critical but stable condition , police said . The father later died in surgery of multiple gunshot wounds .

The oldest of four children , an 8-year-old boy , was the sole family member who was n't injured , police said .

`` What would motivate an individual to do this is inexplicable , '' Inglewood Police Chief Mark Fronterotta said . Inglewood is adjacent to Los Angeles and its international airport .

Police were conducting a manhunt for the suspect , who lived in a house in the rear of the property . That rear house was also set afire , believed to have been ignited by the gunman , police said .

Police did not release names of the father , 30 ; mother , 28 ; or their children as of Saturday afternoon .

The incident occurred about 4 a.m. Saturday when police received a report of 10 gunshots at the property . The fire department also received a call at the same time .

Firefighters were hampered by fears that the gunman might have been armed in the rear residence , police said . Fallen power lines also hindered firefighting efforts .

The suspect was described as a 55-year-old black man with a dark baseball cap and is 5-foot-6 and 160 pounds , police said . They later identified him as Desmond John Moses .

The suspect wore a painter 's mask when he gunned down the family , the police chief said .

Police did n't provide a motive .

The suspect should be considered armed and dangerous , the police chief said .

Police find body in burned California home after family killings

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NEW : Police identify the suspected gunman as 55-year-old Desmond John Moses

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A mother runs from the house carrying her youngest child though she 's shot in both legs

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The 4-year-old boy , shot in the head , later dies in surgery

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The father died after using his body as a shield over his other children